Example 1.2 (Community Detection in Weighted Graphs
(Section REF )) 
One of the most relevant features of graphs representing real systems
is community structure, or clustering, i.e., the
organization of vertices in clusters, with many edges joining
vertices of the same cluster and comparatively few edges joining
vertices of different clusters.
Such communities can be considered as independent components of a
graph, that play a very similar role, e.g., the tissues or the organs
in the human body. Community detection finds applications in a wide and
diverse set of areas such as biology, sociology, and computer science,
to name a few, where systems are often represented as graphs. This
problem is extremely hard and has not yet been solved satisfactorily,
despite the huge effort of a large interdisciplinary community of
scientists working on it over the past few years. This task gets even
harder when having to identify such communities in weighted directed
graphs. We refer the reader to a survey on community
detection [1]} for more details.
